List of top Mathematics Questions on Surface Areas and Volumes asked in JEE Main

From a square of side 30 cm the squares of side x cm is cut off to make a cuboid of maximum volume. The surface area of cuboid with open top is?

The area of the polygon, whose vertices are the non-real roots of the equation \(\bar z = iz^2\) is

Water is being filled at the rate of 1 cm³/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm²/sec) at which the wet conical surface area of the vessel increase, is

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is

Let the area of the triangle with vertices \(A(1, α), B(α, 0)\) and \(C(0, α)\) be \(4\) sq. units. If the points \((α, –α), (–α, α)\) and \((α^2, β)\) are collinear, then \(β\) is equal to

Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4} = 1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6\sqrt3\). Then the eccentricity of the ellipse is

The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is: